Thermal imaging measurement of lateral diffusivity and non-invasive material defect detection

ABSTRACT

A system and method for determining lateral thermal diffusivity of a material sample using a heat pulse; a sample oriented within an orthogonal coordinate system; an infrared camera; and a computer that has a digital frame grabber, and data acquisition and processing software. The mathematical model used within the data processing software is capable of determining the lateral thermal diffusivity of a sample of finite boundaries. The system and method may also be used as a nondestructive method for detecting and locating cracks within the material sample.

U.S. GOVERNMENT RIGHTS

The United States Government has rights in this invention pursuant toContract No. W-31-109-ENG-38 between the U.S. Department of Energy andUniversity of Chicago.

BACKGROUND OF THE INVENTION

Thermal diffusivity, is a material property and relates to the transientheat transfer speed through the particular material. This property isdependent on the heat transfer direction for anisotropic materials.Anisotropic materials are materials that have different properties alonglines of different directions. For planar samples, the normal thermaldiffusivity is a property of the speed at which heat is transferredthrough the thickness of the sample from the side where the heat isapplied to the side where heat was not applied. Lateral thermaldiffusivity is a property of the speed at which heat is transferred in aperpendicular direction within the material relative to the directionfrom which the heat has been applied.

An infrared thermal imaging system is used to determine values fornormal and lateral thermal diffusivity of a material sample. Thermalimaging systems typically consist of an infrared camera, a personalcomputer (PC) equipped with a digital frame grabber and data acquisitionand processing software, a flash lamp as a heat source, and electronicsto monitor and control the system operation. Using this equipment, aflash thermal imaging test is performed. During the test, pulsed heatenergy is applied to the sample's back surface that has been partiallyshielded to prevent a portion of the material sample from being heateddirectly when the pulsed heat energy is applied. The change intemperature distribution on the opposite, front, surface is monitored bythe infrared camera with a series of thermal images being captured andrecorded within the PC.

The temperature distribution represents the effects of both the normalheat transfer through the thickness of the sample and the lateral heattransfer through the interface between the shielded and unshieldedback-surface regions. The temperature distributions that are detectedand recorded by the infrared camera are fitted with a theoreticalsolution of the heat transfer process to determine the lateral thermaldiffusivity at the interface.

Zhong Ouyang, et. al. have published a method for measuring the lateralthermal diffusivity. Their theory was based on samples beinginfinite-sized plates, and required the manual fitting of theexperimental data with the theoretical solution in spatial domain forsingle curves. Their theory also required the interface location to bepre-measured by hand and required even (uniform) heating. A solution forsemi-infinite width (0<×<∞) sample was used by Ouyang et al. (1998), as:${{T\left( {x,L,t} \right)} = {\frac{1}{2L}{\left( {{{erfc}\quad \frac{a - x}{2\sqrt{\alpha_{x}t}}} + {{erfc}\quad \frac{a + x}{2\sqrt{\alpha_{x}t}}}} \right)\left\lbrack {1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}{\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}}}} \right\rbrack}}},$

where T is temperature; x is a point along an x-axis; L is samplethickness; t is time; a is the interface location along the x-axis;α_(x), and α_(z) are the lateral (along the x-axis) andthrough-thickness (along the z-axis) thermal diffusivities,respectively; and n corresponds to the number of terms used in thesummation.

The present system and method for determining normal and lateral thermaldiffusivity uses finite boundaries to determine the diffusivity.Ouyang's method simplifies the determination by using semi-infiniteboundaries. The present system takes non-uniform heating intoconsideration by explicitly calculating the temperature amplitude ateach pixel. The present system may also be used as a nondestructivemethod to detect and locate material defects within the sample (cracksperpendicular to the sample surface). The depth of a crack within thematerial can be determined by the defect's correlating diffusivityvalue. Existing nondestructive techniques for detecting material defectsinclude ultrasound technology. However, ultrasound techniques are timeconsuming for detecting this type of defect in large material samples.

Transient thermography has been used for the nondestructive detection ofmaterial flaws (see U.S. Pat. No. 5,711,603, Ringermacher et al.(“'603”). The '603 patent describes a method for flaw depth detectionusing thermal imaging captured by an infrared camera. The thermalimaging technique used in the '603 patent applies pulsed thermal energyto the sample surface and subsequently a thin layer of material on thesurface will be instantaneously heated to a high temperature. Heattransfer takes place from the surface that was heated to the interior ofthe sample resulting in a continuous decrease of the surfacetemperature. If a plain crack (a crack with a plane parallel to thesample surface that was heated) exists, the heat is restricted fromfurther transfer deeper into the sample material. Therefore, the surfacetemperature at this region will remain higher than in surrounding areasso that the sample material above the plain crack will be viewed as a“hot spot” by the infrared receptors. The hot spot will occur earlierduring the analysis if the crack is shallow and will appear later in theanalysis if the crack is deeper. In '603 a correlation was developedbetween the measured time when the highest hot spot contrast occurs andrelative depth of the crack within the sample. The analysis wasperformed pixel by pixel and the final relative depth for all pixels iscomposed into an image (or map). The relative depth is color coded andpresented as the result.

Differences between the ′603 patent and the present system include thetype of crack or defect that may be detected. The '603 patent detectsplain cracks that are completely within the material and are orientedparallel to the heated sample surface (like an air gap or delaminationdefect). The present invention detects cracks that are perpendicular tothe heated surface and these cracks may be of varying depths thatinclude surface cracks. The '603 patent uses an empirical correlationbetween time of hot spot occurrence and crack depth. The present systemfits experimental temporal-spatial curves with a theoretical model. The'603 patent also derives an image of relative depth of defect from thesurface while the present system derives the depth (or length) of thecrack extending from the surface to the inside of the sample.

OBJECTS OF THE INVENTION

The object of this invention is to provide an automated and accuratemethod for determining the lateral thermal diffusivity of a materialsample using a model that contains finite boundaries.

Another object of this invention is to provide a nondestructive methodfor the detection of cracks within a material sample by use of themethod used to determine thermal diffusivity.

SUMMARY OF THE INVENTION

A system and method for determining lateral thermal diffusivity of amaterial sample using a heat pulse; a sample oriented within anorthogonal coordinate system; an infrared camera; and a computer thathas a digital frame grabber, and data acquisition and processingsoftware. The mathematical model used within the data processingsoftware is capable of determining the thermal diffusivity of a sampleof finite boundaries. The system and method may also be used as anondestructive method for detecting and locating cracks within thematerial sample.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is the system set up for determining diffusivities.

FIG. 2 depicts infrared images taken at t=0.1 s and t=1.0 s after theheat pulse for a ceramic composite.

FIG. 3 depicts the measured temperature distributions at t=0.25 and 0.95s after flash along a typical horizontal line shown in FIG. 2.

FIG. 4 is a comparison of predicted and experimental temperaturedistributions at t=0.25 s and 0.95 s.

FIG. 5 depicts predicted α_(x), and α distributions along they-direction for the ceramic composite sample of FIGS. 2 and 3.

FIG. 6 shows an aluminum alloy sample with a cut of three differentdepths.

FIG. 7 is the system set up for NDE testing of the aluminum alloysample.

FIG. 8 is a schematic of the surface viewed by the infrared cameraindicating expected heat flows.

FIG. 9 is a thermal image taken at t=0.17 s after the heat pulse for thealuminum alloy sample of FIGS. 6 and 7.

FIG. 10 depicts predicted α_(x) along the y-direction for the aluminumalloy sample of FIGS. 6 and 7.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

FIG. 1 depicts the system set up 10. A material sample 20 is placedbetween a heat source 40, that has an average direction of heat flow 42when the heat source 40 is activated, and an infrared camera 50 that hasinfrared receptors directed toward the sample 20. The sample 20 isoriented within an orthogonal coordinate system having x, y, and z-axes.The x-y plane of the coordinate system is perpendicular to the averagedirection of heat flow 42 while the z-axis is essentially parallel tothe average direction of heat flow 42. A shield 22 on the back side (theside facing the heat source 40) of the sample 20 insulates the portionof the sample 20 that is covered by the shield 22 from receiving heatfrom the heat source 40 when the heat source 40 is activated. An edge ofthe shield 22 creates an interface 32 between the shielded portion ofthe sample 28 and the unshielded portion of the sample 30. The interface32 is essentially equidistant from the y-axis. The infrared camera 50 iscoupled to a personal computer (PC) 60. The PC 60 is equipped with adigital frame grabber and data acquisition and data processing software.

To determine lateral thermal diffusivity using this set up 10, the heatsource 40 is activated and a heat pulse heats the unshielded portion ofthe sample 30. The unshielded portion of the sample 30 absorbs the heatpulse and heat energy is diffused through the sample at a ratedetermined by the specific properties of the material that makes up thesample 20. Heat energy diffuses in the z-direction (through the sample's20 thickness) and laterally (in the x-direction). Methods forthrough-thickness (normal) diffusivity, α_(z), were developed in the1960s. Therefore, the normal thermal diffusivity is not directlymeasured using this set up 10 because such values are readily availableand are considered known values for the samples. There will be no heatflow through the sample 20 in the y-direction using this system 10 witha flat rectangular sample 20 unless the sample 20 contains internaldefects.

Previous techniques can not process thermal data with a non-uniformheating effect. For any technique, the experimental set-up should bedesigned to provide as uniform heating as possible. However, non-uniformheating may be the result of varying optical properties on the surfaceof a single sample. For example, a black surface usually exhibits highsurface absorptivity, the ceramic composite sample used for data inFIGS. 2-5 should have an absorptivity larger than 0.9 (maximumabsorptivity is 1.0). If a sample has surface contamination and one partof the sample has an absorptivity of 0.8 and another part of 0.9, thenafter heating, the first part may reach a surface temperature of 80° C.,but the second part will have a surface temperature of 90° C. (this maybe considered non-uniform heating). The present invention handles thesetemperature differences by explicitly calculating the temperatureamplitude at each pixel.

As the heat energy diffuses through the sample 20 with time, theinfrared camera 50 receives thermal images in a 256×256 focal planearray of infrared detectors. Therefore there are 256 pixels along thex-axis and 256 pixels along the y-axis of the sample 20. The digitalframe grabber software on the PC 60 stores the images. The dataacquisition and data processing software will record individualtemperature values of the sample 20 as perceived at each pixel withinthe infrared camera 50. The recorded temperature and correspondinglocation on the sample 20 will be compared to a theoretical temperaturedistribution according to the equation: $\begin{matrix}{{T\left( {x,L,t} \right)} = {{\frac{a}{XL}\left\lbrack {1 + {2{\sum\limits_{m = 1}^{\infty}{\frac{X}{m\quad \pi \quad a}\sin \quad \frac{m\quad \pi \quad a}{X}\cos \quad \frac{m\quad \pi \quad x}{X}{\exp \left( {{- \frac{m^{2}\pi^{2}}{X^{2}}}\alpha_{x}t} \right)}}}}} \right\rbrack}{{\left\lbrack {1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}{\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}}}} \right\rbrack,}}}} & \left( {{Eq}.\quad 1} \right)\end{matrix}$

where T is theoretical temperature; x is a corresponding point along thex-axis; L is the thickness of the sample 20 along the z-axis; X is theoverall width of the sample 20; t is time; a is the interface location32 along the x-axis; α_(x) and α_(z) are a lateral (along said x-axis)and a normal (along said z-axis) thermal diffusivity, respectively; andm and n correspond to the number of terms used in their respectivesummations.

Equation 1 is derived for the heat transfer process as examined underideal conditions, this equation should match perfectly with theexperimental data (for every pixel and at every time instant) providedthat all parameters used in this equation are correct. Parametersalready known include: sample thickness L, sample width X,through-thickness diffusivity α_(z), as these values are previouslymeasured; we also know pixel position x_(i) and time t when each imageis taken. The only unknown parameters in the above equation are α_(x)and α. The main objective of this invention is to find the correctvalues of α_(x) and a so the theoretical curve (calculated from theabove equation) will have a best match of experimental data (curves).

FIG. 2 depicts two typical thermal images taken at times t=0.1 s andt=1.0 s (the complete set of data contains 101 images taken at t=0,0.01, 0.02, . . . 1.0 s). The images in FIG. 2 each have 185 pixels inthe x-direction (width) and 80 pixels in the y-direction (height).Therefore, the corresponding data has 80×185-pixel lines withtemperature distributions measured at intervals of 0.01 s from t=0 s tot=1 s for each line. If the sample 20 is uniform, the lateral heattransfer occurs only in the x-direction and lateral thermal diffusivityis a constant at any y location. This situation is the ideal2-dimensional heat transfer condition as assumed in Eq. 1 above. Underthese conditions, the heat transfer data at one y= constant line may beanalyzed to determine α_(x) as the lateral thermal diffusivity at x=α.When the sample 20 is not uniform (due to material variation or defect),every y= constant line (all 80 lines for the sample shown in FIG. 2)must be analyzed to obtain an α_(x) distribution along the interfaceline (along the y-direction), i.e., α_(x) distribution in 0<y<Y at ×=α.

Data processing for each line begins with inputting initially estimatedvalues for lateral thermal diffusivity, α_(x), and interface location,a. The analysis is performed one line at a time.

The goal is to fit the theoretical temperature distribution curves fromEq. 1 with measured temperature distributions at all time steps. Thebest fit between the theoretical and measured distributions gives thecorrect lateral thermal diffusivity, α_(x), and interface location, a.FIG. 3 illustrates the measured temperature distributions at t=0.25 sand t=0.95 s for the images shown in FIG. 2 after the heat pulse wasreleased from the heat source 40.

To fit the theoretical distribution with the measured temperaturedistribution for each pixel, the values for lateral diffusivity, α_(x),and interface location, a, are initially estimated and the theoreticaltemperature value from Eq. 1 above is compared with the measured andrecorded value for each x location by use of a least-square fitequation: $\begin{matrix}{F = {\sum\limits_{t}{\sum\limits_{i}{{w_{i}\left\lbrack {{A_{i}{T\left( {x_{i},L,t} \right)}} - {T_{i}(t)}} \right\rbrack}^{2}.}}}} & \left( {{Eq}.\quad 2} \right)\end{matrix}$

The initially guessed values for a and a are inserted into Equation 1 toobtain a temperature at every pixel and every time instant. The totalerror between the calculated temperature and measured temperature is Fas determined by Equation 2. When there is a perfect match (idealcondition and with correct values of α_(x) and α), F=0; but due toexperimental noise and/or other factors, F is always experimentallylarger than zero. The minimum F (i.e., at the smallest match error)should give the correct values of α_(x) and α. The Newton method is thenused to derive a new guess of α_(x) and a values so F is minimized, thisis one cycle of the iteration. Many iterations are needed to finallyobtain the correct α_(x) and a values such that F is minimized.

For the example shown in FIGS. 2 and 3, at pixel i (0≦i≦184), denote A,as temperature amplitude to be determined and x, as x-coordinate atpixel i, then the theoretical temperature prediction A_(i)T(x_(i), L, t)(where T(x_(i), L, t) is from Eq. 1) and measured temperature T_(i)(t)(obtained from thermal imaging data) as functions of time (at times t=0,0.01, 0.02, , 1.0 s). Because both T(x_(i), L, t) and T_(i)(t) areknown, a simple least-square fit of these two time-history curvesdetermines the amplitude A_(i) at pixel i. This process is repeated toobtain A_(i) for all pixels in the current horizontal line.

The thermal imaging data in FIG. 3 show that the change of temperaturedue to lateral heat transfer occurs only near the interface location atx=a. Therefore, when performing data fitting, the data near theinterface 32 should receive bigger weight than those far away from theinterface 32. By doing so, the fitting accuracy will be improved. Toestablish the weighting function, the slope of each temperaturedistribution curve (along x-direction at fixed time) is calculated. Theslope curves at all time steps are then averaged and normalized (i.e.,maximum at 1), and the area under the average-normalized slope curve iscalculated (denoted as W). The weighting function is then defined as anormal distribution function centered at a: $\begin{matrix}{{{w_{i} = {{{\exp \left\lbrack {- {\pi \left( \frac{x_{i} - a}{W} \right)}^{2}} \right\rbrack}\quad 0} \leq i \leq 184}},}\quad} & \left( {{Eq}.\quad 3} \right)\end{matrix}$

where a is the interface location 32.

After fitting function F is calculated from Eq. 2, new α_(x) and αvalues are predicted by Newton iteration scheme to minimize F. These newvalues are used as new guesses in next iteration. Iterations of thistype continue until F is minimized (or approaches the best fit). Thepredicted α_(x) and α values converge to the correct values when usingsimulated analytical data. A comparison of predicted and experimentaltemperature distributions is shown in FIG. 4.

The steps of initially guessing values for α_(x) and α; determining thetemperature amplitude at each pixel; applying a weighting function;applying a fitting function; and iterations to determine α_(x) and α,can be repeated for all lines in the y-direction (80 lines for theexample shown in FIGS. 2 and 3). FIG. 5 shows the predicted α_(x) and αdistributions along the y-direction for the ceramic composite sampleused in FIGS. 2 and 3.

Nondestructive evaluation (NDE) or detection of cracks within the sample20 can be accomplished using this system 10. Through-thickness cracksare typically not detected by through-thickness NDE techniques such asthrough-thickness (normal) thermal diffusivity, transmission ultrasound,and x-ray imaging. However, such cracks or defects can easily bedetected and characterized by lateral thermal diffusivity measurement.

FIG. 6 shows an aluminum alloy sample with a vertical cut of threedepths at the middle width (x-direction). The target cut depths are ¾,½, and ¼ of the thickness and each cut length is ¼ of the sample height(y-direction). There is not a cut at the bottom ¼ of the height. The setup for NDE is shown in FIG. 7. The cut surface faces the heat source 40and the smooth surface faces the infrared camera 50. The interface isvertical along the cut. It is expected that the heat will diffuse in thelateral y-direction in addition to diffusing in the x-direction becausethe dominant lateral heat flow in the x-direction is not uniform. Anillustration of this heat flow scheme is shown in FIG. 8. They-direction heat flow will reduce the sensitivity and resolution indetecting the tip of the defect where the depth of the cut changes.

FIG. 9 shows a thermal image taken at 0.17 s after the heat pulse hasbeen delivered. It is evident that the heat flow is stronger at thebottom of the image than at the top because the cut is deeper at thetop. The predicted lateral thermal diffusivity α_(x) along the sampleheight (y-direction) is plotted in FIG. 10. The average values of α_(x)at all four regions of thickness are plotted at dotted lines and arelisted in Table 1.

TABLE 1 List of predicted values of lateral thermal diffusivity α_(x)Cut depth (%) Predicted α_(x) (mm²/s) α_(x) reduction (%) 0 70 0 25 6014 50 45 36 75 25 64

The predicted lateral thermal diffusivity is sensitive to cut depth. Itshould be noted that cut depths listed in Table 1 are target values formachining and could not be directly measured due to the thinness of thesample and the cut width. The sample can be scanned for cracks byplacing the vertical shielding material at various x-locations and theresulting α_(x) distributions (each as that in FIG. 10) can be plottedinto a 2-dimensional image to reveal the location and intensity of thethrough-thickness defect.

What is claimed is:
 1. A system for determining thermal diffusivity in amaterial sample, comprising: a heat source having an average directionof heat flow directed toward a plurality of infrared receptors associatewith an infrared camera; where said infrared receptors are directed inapproximate opposition to said average direction of heat flow from saidheat source; a sample located between said heat source and said infraredcamera such that said sample intercepts a heat flow from said heatsource, said sample having a back side and a front side with said backside facing said heat source and said front side facing said infraredcamera, said sample defining an orientation of an orthogonal coordinatesystem having axes x, y and z, such that an x-y plane of said coordinatesystem is perpendicular to said average direction of said heat flow fromsaid heat source when said heat source is energized and where said zaxis is essentially parallel to said average direction of heat flow; aheat insulating shield positioned to cover a portion of said back sideof said sample where said heat shield is sized to cover all of saidsample located behind said heat shield providing a shielded sampleportion and where an interface edge of said shield defines an interfacebetween said shielded sample portion of said sample and an unshieldedsample portion which comprises the remainder of said sample in said x-yplane where said interface edge extends across said sample along alinear axial projection effectively bisecting said sample along an axialline; and a computer coupled to said infrared camera, said computerhaving a plurality of software capable of data acquisition and dataprocessing where said computer receives and records temperature changeswith time as sensed by said infrared receptors after a pulse of heat hasbeen emitted from said heat source and compares said recordedtemperatures within an equation:${T\left( {x,L,t} \right)} = {{\frac{a}{X\quad L}\left\lbrack {1 + {2{\sum\limits_{m = 1}^{\infty}{\frac{X}{m\quad \pi \quad a}\sin \quad \frac{m\quad \pi \quad a}{X}\cos \quad \frac{m\quad \pi \quad x}{X}{\exp \left( {{- \frac{m^{2}\pi^{2}}{X^{2}}}\alpha_{x}t} \right)}}}}} \right\rbrack}\left. \left\lbrack 1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}} \right. \right\rbrack}$

when said interface is oriented along a designated y axis partlycovering said sample and where T is temperature; x is a point along saidx axis; L is a sample thickness measured along said z axis; t is time; Xis a width of said sample as measured along said x axis; α_(x) and α_(z)are a lateral (along said x-axis) and a normal (along said z-axis)thermal diffusivity, respectively; and m and n correspond to a number ofterms used in a respective summation where said equation is numericallysolved for said lateral and said normal diffusivities.
 2. A method fordetermining lateral thermal diffusivity in a material sample, comprisingthe steps of: positioning a heat source so that when said heat source isenergized it produces a heat flow having an average direction of heatflow; positioning an infrared camera having a plurality of infraredreceptors such that said infrared receptors are directed in oppositionto said average direction of heat flow; positioning a sample betweensaid heat source and said camera and at a specified distance from saidheat source and within an orthogonal coordinate system having an originand axes x, y and z, such that an x-y plane of said coordinate system isperpendicular to said average direction of said heat flow from said heatsource when said heat source is energized and where said z axis isessentially parallel to said average direction of heat flow; selecting aheat shield having a straight linear edge or interface, a continuousunpenetrated surface and sized so that said heat shield equals orexceeds said sample in surface area within said x-y plane allowing saidheat shield to completely cover a portion of said sample not selectivelyexposed by positioning said interface of said heat shield with theresult that said heat shield effectively divides said sample into ashielded portion and an unshielded portion along said interface; placingsaid heat shield on a back side of said sample facing said heat sourceand and orienting said heat shield so that said straight edge orinterface is parallel with said y axis; placing said interface at adistance “a” from said y axis as measured along said x axis so that aplurality of points along said interface are equidistant from said yaxis; applying a pulse of heat energy from said heat energy source tosaid sample such that an unshielded area absorbs part of said energywhile said shielding material prevents a shielded area from absorbingpart of said energy; receiving a digitized thermal image of said samplewith time as said energy diffuses through said sample where said imageis generated by thermal information sensed by infrared receptorsincorporated in said camera on a front side of said sample; recording adigitized thermal image of of said sample with time as said energydiffuses through said sample from said back side to said front side;numerically generating a theoretical temperature distribution, T,response over time, t, through a thickness, L, of said sample accordingto an equation:${{T\left( {x,L,t} \right)} = {{\frac{a}{X\quad L}\left\lbrack {1 + {2{\sum\limits_{m = 1}^{\infty}{\frac{X}{m\quad \pi \quad a}\sin \quad \frac{m\quad \pi \quad a}{X}\cos \quad \frac{m\quad \pi \quad x}{X}{\exp \left( {{- \frac{m^{2}\pi^{2}}{X^{2}}}\alpha_{x}t} \right)}}}}} \right\rbrack}\left. \left\lbrack 1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}} \right. \right\rbrack}};$

where x is a point along said x-axis; X is a sample width; α_(x) andα_(z) are a lateral (along said x-axis) and a normal (along said z-axis)thermal diffusivity, respectively; and m and n correspond to a number ofterms used in a respective summation; fitting said theoreticaltemperature distribution with a measured temperature distribution ateach of several time steps and for each of several pixels by: inputtinginitially guessed values for a_(x) and a into said equation; andcomparing said theoretical temperature value from said equation for eachvalue of x with said recorded temperature value at each x location byuse of a least-square fit of said temperature values; and numericallysolving said equation for said interface, and said lateral diffusivity.3. The method according to claim 2, further comprising the step of:obtaining a modulation distribution by applying said equation to fit atemporal datum at each of several pixels within said infrared camera toderive a temperature amplitude, A_(i), at each of said pixels.
 4. Themethod according to claim 3, further comprising the step of: assigninglarger weight to a datum that is closer to said interface located at a,as compared to a datum that is farther away from said interface byapplying a weighting function as a normal distribution function centeredat said interface, a to each of said datum points generated by saidthermal imaging:$w_{i} = {\exp \left\lbrack {- {\pi \left( \frac{x_{i} - a}{W} \right)}^{2}} \right\rbrack}$

where W is an area under an average, normalized slope curve of measuredtemperature distributions and w_(I) is a weighting function used to biasa set of obtained data so that data obtained in a neighborhood of apoint close to said interface is given a greater weight than one furtheraway from said interface; employing said weighting function in aniterative technique to determine a correct value for said lateraldiffusivity, α_(x), through the use of an equation for calculating atotal error between a calculated temperature and a measured temperature,F, where$F = {\sum\limits_{t}{\sum\limits_{i}{w_{i}\left\lbrack {{A_{i}{T\left( {x_{i},L,t} \right)}} - {T_{i}(t)}} \right\rbrack}^{2}}}$

A_(i)=Temperature Amplitude; T(x_(i),L, t)=Temperature as calculated inclaim 2; T_(i)(t)=Measured temperature from thermal imaging; t=Time; andi=Location designator.
 5. The method according to claim 2, wherein saidmaterial sample is selected from a group consisting of: metal alloys andcontinuous fiber ceramic composites.
 6. The method according to claim 2,wherein said shielding material is a material that insulates said samplefrom said heat source.
 7. The method according to claim 2, wherein saidheat energy source is a flash lamp.
 8. The method according to claim 2,wherein said infrared camera has a focal plane array of 256×256 InSb(Indium Antimonide) sensors.
 9. A method for determining lateral thermaldiffusivity in a material sample, comprising the steps of: positioning aheat source so that when said heat source is energized it produces aheat flow having an average direction of heat flow; positioning aninfrared camera such that an infrared receptor for said camera isdirected in opposition to said average direction of heat flow;positioning a sample between said heat source and said camera and at aspecified distance from said heat source and within an orthogonalcoordinate system having axes x, y and z, such that an x-y plane of saidcoordinate system is perpendicular to said average direction of saidheat flow from said heat source when said heat source is energized andwhere said z axis is essentially parallel to said average direction ofheat flow; placing a shielding material on a back side of said samplefacing said heat source and from an edge of said sample such thatinterface, a, is defined where a is measured along said x axis such thatsaid interface, a, is equidistant along said y axis as measured fromsaid x axis; applying a pulse of heat energy from said heat energysource to said sample such that an unshielded area absorbs part of saidenergy while said shielding material prevents a shielded area fromabsorbing part of said energy; receiving a digitized thermal image ofsaid sample with time as said energy diffuses through said sample wheresaid image is generated by thermal information sensed by infraredreceptors incorporated in said camera on a front side of said sample;recording a digitized thermal image of of said sample with time as saidenergy diffuses through said sample from said back side to said frontside; numerically generating a theoretical temperature distribution, T,response over time, t, through a thickness, L, of said sample accordingto an equation:${{T\left( {x,L,t} \right)} = {{\frac{a}{X\quad L}\left\lbrack {1 + {2{\sum\limits_{m = 1}^{\infty}{\frac{X}{m\quad \pi \quad a}\sin \quad \frac{m\quad \pi \quad a}{X}\cos \quad \frac{m\quad \pi \quad x}{X}{\exp \left( {{- \frac{m^{2}\pi^{2}}{X^{2}}}\alpha_{x}t} \right)}}}}} \right\rbrack}\left. \left\lbrack 1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}} \right. \right\rbrack}};$

where x is a point along said x-axis; X is a sample width; α_(x) andα_(z) are a lateral (along said x-axis) and a normal (along said z-axis)thermal diffusivity, respectively; and m and n correspond to a number ofterms used in a respective summation; fitting said theoreticaltemperature distribution with a measured temperature distribution ateach of several time steps and for each of several pixels by: inputtinginitially guessed values for a_(x) and a into said equation; andcomparing said theoretical temperature value from said equation for eachvalue of x with said recorded temperature value at each x location byuse of a least-square fit of said temperature values; assigning largerweight to a datum that is closer to said interface located at a, ascompared to a datum that is farther away from said interface by applyinga weighting function as a normal distribution function centered at saidinterface, a to each of said datum points generated by said thermalimaging:$w_{i} = {\exp \left\lbrack {- {\pi \left( \frac{x_{i} - a}{W} \right)}^{2}} \right\rbrack}$

where W is an area under an average, normalized slope curve of measuredtemperature distributions; fitting said temperature, T, distributions atall time steps, t, to determine an interface location, a_(;) fittingsaid temperature, T, distributions at all time steps, t, to determine avalue for lateral thermal diffusivity, α_(x); and determining a lateraldiffusivity distribution along said interface at x=a by calculating theα_(x) and a at each of several lines defined by y is constant.
 10. Amethod for determining lateral thermal diffusivity in a material sample,comprising the steps of: positioning a heat source so that when saidheat source is energized it produces a heat flow having an averagedirection of heat flow; positioning an infrared camera such that aninfrared receptor for said camera is directed in opposition to saidaverage direction of heat flow; positioning a sample between said heatsource and said camera and at a specified distance from said heat sourceand within an orthogonal coordinate system having axes x, y and z, suchthat an x-y plane of said coordinate system is perpendicular to saidaverage direction of said heat flow from said heat source when said heatsource is energized and where said z axis is essentially parallel tosaid average direction of heat flow; placing a shielding material on aback side of said sample facing said heat source and from an edge ofsaid sample such that interface, a, is defined where a is measured alongsaid x axis such that said interface, a, is equidistant along said yaxis as measured from said x axis; applying a pulse of heat energy fromsaid heat energy source to said sample such that an unshielded areaabsorbs part of said energy while said shielding material prevents ashielded area from absorbing part of said energy; receiving a digitizedthermal image of said sample with time as said energy diffuses throughsaid sample where said image is generated by thermal information sensedby infrared receptors incorporated in said camera on a front side ofsaid sample; recording a digitized thermal image of of said sample withtime as said energy diffuses through said sample from said back side tosaid front side; numerically generating a theoretical temperaturedistribution, T, response over time, t, through a thickness, L, of saidsample according to an equation:${{T\left( {x,L,t} \right)} = {{\frac{a}{X\quad L}\left\lbrack {1 + {2{\sum\limits_{m = 1}^{\infty}{\frac{X}{m\quad \pi \quad a}\sin \quad \frac{m\quad \pi \quad a}{X}\cos \quad \frac{m\quad \pi \quad x}{X}{\exp \left( {{- \frac{m^{2}\pi^{2}}{X^{2}}}\alpha_{x}t} \right)}}}}} \right\rbrack}\left. \left\lbrack 1 + {2{\sum\limits_{n = 1}^{\infty}{\left( {- 1} \right)^{n}\exp \left( {{- \frac{n^{2}\pi^{2}}{L^{2}}}\alpha_{z}t} \right)}}} \right. \right\rbrack}};$

where x is a point along said x-axis; X is a sample width; α_(x) andα_(z) are a lateral (along said x-axis) and a normal (along said z-axis)thermal diffusivity, respectively; and m and n correspond to a number ofterms used in a respective summation; fitting said theoreticaltemperature distribution with a measured temperature distribution ateach of several time steps and for each of several pixels by: inputtinginitially guessed values for a_(x) and a into said equation; andcomparing said theoretical temperature value from said equation for eachvalue of x with said recorded temperature value at each x location byuse of a least-square fit of said temperature values; fitting saidtemperature, T, distributions at all time steps, t, to determine aninterface location a; fitting said temperature, T, distributions at alltime steps, t, to determine a value for lateral thermal diffusivity,α_(x); and determining a lateral diffusivity distribution along saidinterface at x=a by calculating the α_(x) and a at each of several linesdefined by y is constant.
 11. The method according to claim 10, furthercomprising the step of: detecting defects within said sample byobserving an infrared thermal image captured by said infrared camera andnoting differences in thermal diffusivity along a y-axis.
 12. The methodaccording to claim 11, further comprising the step of: scanning saidsample for defects by placing said shielding at various locations alongan x-axis.